The context of this research is multiobjective optimization where conflicting objectives are present. In this work, these objectives are only available as the outputs of a blackbox for which no derivative information is available. This work proposes a new extension of the mesh adaptive direct search (MADS) algorithm to multiobjective derivative-free optimization with bound constraints. This method does not aggregate objectives and keeps a list of non dominated points which converges to a (local) Pareto set as long as the algorithm unfolds. As in the single-objective optimization MADS algorithm, this method is built around a search step and a poll step. Under classical direct search assumptions, it is proved that the so-called DMulti-MADS algorithm generates multiple subsequences of iterates which converge to a set of local Pareto stationary points. Finally, computational experiments suggest that this approach is competitive compared to the state-of-the-art algorithms for multiobjective blackbox optimization.

这项研究的背景是存在冲突目标的多目标优化。在这项工作中，这些目标仅可用作黑匣子的输出，而黑匣子的输出则没有可用的派生信息。这项工作提出了一种新的网格自适应直接搜索（MADS）算法扩展，使其具有约束约束的多目标无导数优化。这种方法不会汇总目标，并且会保留未支配点的列表，只要算法展开，这些支配点将收敛到（局部）Pareto集。与单目标优化MADS算法一样，此方法围绕搜索步骤和轮询步骤构建。在经典直接搜索假设下，证明了所谓的DMulti-MADS算法会生成多个迭代子序列，这些子序列收敛到一组局部Pareto平稳点。